103 lines
3.3 KiB
C#
103 lines
3.3 KiB
C#
// Copyright 2010-2022 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// [START program]
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// OR-Tools solution to the N-queens problem.
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// [START import]
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using System;
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using Google.OrTools.ConstraintSolver;
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// [END import]
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public class NQueensCp
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{
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public static void Main(String[] args)
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{
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// Instantiate the solver.
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// [START solver]
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Solver solver = new Solver("N-Queens");
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// [END solver]
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// [START variables]
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const int BoardSize = 8;
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IntVar[] queens = new IntVar[BoardSize];
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for (int i = 0; i < BoardSize; ++i)
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{
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queens[i] = solver.MakeIntVar(0, BoardSize - 1, $"x{i}");
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}
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// [END variables]
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// Define constraints.
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// [START constraints]
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// All rows must be different.
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solver.Add(queens.AllDifferent());
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// All columns must be different because the indices of queens are all different.
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// No two queens can be on the same diagonal.
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IntVar[] diag1 = new IntVar[BoardSize];
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IntVar[] diag2 = new IntVar[BoardSize];
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for (int i = 0; i < BoardSize; ++i)
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{
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diag1[i] = solver.MakeSum(queens[i], i).Var();
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diag2[i] = solver.MakeSum(queens[i], -i).Var();
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}
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solver.Add(diag1.AllDifferent());
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solver.Add(diag2.AllDifferent());
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// [END constraints]
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// [START db]
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// Create the decision builder to search for solutions.
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DecisionBuilder db = solver.MakePhase(queens, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
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// [END db]
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// [START solve]
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// Iterates through the solutions, displaying each.
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int SolutionCount = 0;
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solver.NewSearch(db);
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while (solver.NextSolution())
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{
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Console.WriteLine("Solution " + SolutionCount);
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for (int i = 0; i < BoardSize; ++i)
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{
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for (int j = 0; j < BoardSize; ++j)
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{
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if (queens[j].Value() == i)
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{
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Console.Write("Q");
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}
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else
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{
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Console.Write("_");
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}
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if (j != BoardSize - 1)
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Console.Write(" ");
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}
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Console.WriteLine("");
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}
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SolutionCount++;
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}
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solver.EndSearch();
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// [END solve]
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// Statistics.
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// [START statistics]
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Console.WriteLine("Statistics");
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Console.WriteLine($" failures: {solver.Failures()}");
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Console.WriteLine($" branches: {solver.Branches()}");
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Console.WriteLine($" wall time: {solver.WallTime()} ms");
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Console.WriteLine($" Solutions found: {SolutionCount}");
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// [END statistics]
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}
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}
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// [END program]
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